Solve for three vectors from three vector equations

[rphmy]

V1–V2 +V3 = 2i+2j+3k, V1– 2V2-2V3 = -5i+7j+8k, and V1+V2+V3 = 4i-2j-k

a) Find V1,V2, and V3

b) Find V=V1+V3 in terms of its components. What is the magnitude and direction of V?


All I know is that they are three dimensional vectors.

Any help will be much appreciated

 

[odie5533]

$$\vec{V}_{1} = 2\hat{i} + 2\hat{j} + 3\hat{k} + \vec{V}_{2} - \vec{V}_{3}$$
Using substitution you should be able to solve for the 3 vectors.

 

[HallsofIvy]

Essentially, you are talking about solving three linear equations for the three unknowns,
V1, V2, and V3. odie5533's suggestion is good. It also appears that if you multiply the equation V1–V2 +V3 = 2i+2j+3k by 2 to get 2V1–2V2 +2V3 = 4i+4j+6k,and add that to the first equation, V1– 2V2-2V3 = -5i+7j+8k, you eliminate V3 from the equations. Treat it exactly like solving simultaneous.